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形状误差分离的根本问题是误差分离方程的求解，其解是否存在，决定了形状误差能否分离．通过对现存的各种圆度、直线度、圆柱度及螺纹导程误差等形状误差分离技术的深入探讨，就形状误差分离技术的共同性质作了归纳，据此提出了在线误差测量和分离的一般方法，给出形式统一的矩阵方程．在此基础上，针对误差分离统一方程解的性质进行了详细讨论，应用矩阵理论给出了误差分离统一方程解的确定性准则．结合形状误差分离技术的具体实现，给出了多点法的测量传感器个数和多步法测量传感器移步步数的统一确定方法．
The fundamental problem of shape error separation is the solution of the error separation equation. Whether its solution exists or not determines the shape error can be separated. Through the discussion of the existing shape error separation techniques such as roundness, straightness, cylindricity and thread lead error, the common properties of shape error separation technology are summarized. Based on this, the on-line error measurement and separation The general method, given the form of a unified matrix equation. On this basis, the properties of the solution to the unified equation of error separation are discussed in detail. The deterministic criterion for the solution to the unified equation of error separation is given using the matrix theory. Combined with the concrete realization of the shape error separation technique, a unified method of determining the number of multi-point measuring sensors and multi-step measuring sensor moving steps is given.